Theorem mulcomi 7591

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 7568	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 418	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1296   e. wcel 1445  (class class class)co 5690   CCcc 7445   x. cmul 7452

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 107  ax-mulcom 7543

This theorem is referenced by:  mulcomli  7592  8th4div3  8733  numma2c  9021  nummul2c  9025  9t11e99  9105  binom2i  10194  fac3  10271  tanval2ap  11168